Tangent power sums and their applications

2012/06/29 by Vladimir Shevelev, Shevelev, Vladimir, Peter J. C. Moses +1
Computer Science · Engineering · Mathematics · #11A63 #Algorithms and Data Compression #FOS: Mathematics #Number Theory (math.NT) #graph theory and CDMA systems #math.NT #msc:11A63 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1207.0404

14 pages. Addition of reference: A.M. and I.M. Yaglom (1953)

openalex publication_date 2012/06/29 · arxiv created 2014/07/31 · arxiv updated 2014/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For integer m, p, we study tangent power sum ∑^m_k=1tan^2p(πk)/(2m+1). We prove that, for every m, p, it is integer, and, for a fixed p, it is a polynomial in m of degree 2p. We give recurrent, asymptotical and explicit formulas for these polynomials and indicate their connections with Newman's digit sums in base 2m.

Citations

• Two algorithms for evaluation of the Newman digit sum, and a new proof of Coquet's theorem

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